private static void test02() //****************************************************************************80 // // Purpose: // // TEST02 tests TETRAHEDRON_NCC_RULE. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 31 January 2007 // // Author: // // John Burkardt // { const int dim_num = 3; int rule; Console.WriteLine(""); Console.WriteLine("TEST02"); Console.WriteLine(" TETRAHEDRON_NCC_RULE returns the points and weights"); Console.WriteLine(" of an NCC rule for the tetrahedron."); Console.WriteLine(""); Console.WriteLine(" In this test, we simply check that the weights"); Console.WriteLine(" sum to 1."); int rule_num = NewtonCotesClosed.tetrahedron_ncc_rule_num(); Console.WriteLine(""); Console.WriteLine(" Number of available rules = " + rule_num + ""); Console.WriteLine(""); Console.WriteLine(" Rule Sum of weights"); Console.WriteLine(""); for (rule = 1; rule <= rule_num; rule++) { int order_num = NewtonCotesClosed.tetrahedron_ncc_order_num(rule); double[] xyztab = new double[dim_num * order_num]; double[] wtab = new double[order_num]; NewtonCotesClosed.tetrahedron_ncc_rule(rule, order_num, ref xyztab, ref wtab); double wtab_sum = 0.0; int order; for (order = 0; order < order_num; order++) { wtab_sum += wtab[order]; } Console.WriteLine(" " + rule.ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + wtab_sum.ToString(CultureInfo.InvariantCulture).PadLeft(14) + ""); } }
private static void test05() //****************************************************************************80 // // Purpose: // // TEST05 demonstrates REFERENCE_TO_PHYSICAL_T4. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 31 January 2007 // // Author: // // John Burkardt // { const int DIM_NUM = 3; const int NODE_NUM = 4; int node; double[] node_xyz = { 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0 }; double[] node_xyz2 = { 4.0, 5.0, 1.0, 6.0, 5.0, 1.0, 4.0, 8.0, 1.0, 4.0, 5.0, 5.0 }; int order; Console.WriteLine(""); Console.WriteLine("TEST06"); Console.WriteLine(" REFERENCE_TO_PHYSICAL_T4 transforms a rule"); Console.WriteLine(" on the unit (reference) tetrahedron to a rule on "); Console.WriteLine(" an arbitrary (physical) tetrahedron."); const int rule = 3; int order_num = NewtonCotesClosed.tetrahedron_ncc_order_num(rule); double[] xyz = new double[DIM_NUM * order_num]; double[] xyz2 = new double[DIM_NUM * order_num]; double[] w = new double[order_num]; NewtonCotesClosed.tetrahedron_ncc_rule(rule, order_num, ref xyz, ref w); // // Here is the reference tetrahedron, and its rule. // Console.WriteLine(""); Console.WriteLine(" The reference tetrahedron:"); Console.WriteLine(""); for (node = 0; node < NODE_NUM; node++) { Console.WriteLine(" " + (node + 1).ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + node_xyz[0 + node * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + node_xyz[1 + node * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + node_xyz[2 + node * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + ""); } double volume = Tetrahedron.tetrahedron_volume(node_xyz); Console.WriteLine(""); Console.WriteLine(" Rule " + rule + " for reference tetrahedron"); Console.WriteLine(" with volume = " + volume + ""); Console.WriteLine(""); Console.WriteLine(" X Y Z W"); Console.WriteLine(""); for (order = 0; order < order_num; order++) { Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + xyz[0 + order * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + xyz[1 + order * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + xyz[2 + order * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + w[order].ToString(CultureInfo.InvariantCulture).PadLeft(14) + ""); } // // Transform the rule. // Tetrahedron.reference_to_physical_t4(node_xyz2, order_num, xyz, ref xyz2); // // Here is the physical tetrahedron, and its transformed rule. // Console.WriteLine(""); Console.WriteLine(" The physical tetrahedron:"); Console.WriteLine(""); for (node = 0; node < NODE_NUM; node++) { Console.WriteLine(" " + (node + 1).ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + node_xyz2[0 + node * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + node_xyz2[1 + node * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + node_xyz2[2 + node * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + ""); } double volume2 = Tetrahedron.tetrahedron_volume(node_xyz2); Console.WriteLine(""); Console.WriteLine(" Rule " + rule + " for physical tetrahedron"); Console.WriteLine(" with volume = " + volume2 + ""); Console.WriteLine(""); Console.WriteLine(" X Y Z W"); Console.WriteLine(""); for (order = 0; order < order_num; order++) { Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + xyz2[0 + order * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + xyz2[1 + order * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + xyz2[2 + order * DIM_NUM].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + w[order].ToString(CultureInfo.InvariantCulture).PadLeft(14) + ""); } }
private static void test06() //****************************************************************************80 // // Purpose: // // TEST06 tests TETRAHEDRON_NCC_RULE. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 31 January 2007 // // Author: // // John Burkardt // { const int dim_num = 3; int o; int s; Console.WriteLine(""); Console.WriteLine("TEST06"); Console.WriteLine(" TETRAHEDRON_NCC_RULE returns the points and weights"); Console.WriteLine(" of an NCC rule for the tetrahedron."); const int rule = 4; Console.WriteLine(""); Console.WriteLine(" In this test, we simply print rule " + rule + ""); int suborder_num = NewtonCotesClosed.tetrahedron_ncc_suborder_num(rule); int[] suborder = NewtonCotesClosed.tetrahedron_ncc_suborder(rule, suborder_num); double[] suborder_w = new double[suborder_num]; double[] suborder_xyz = new double[4 * suborder_num]; NewtonCotesClosed.tetrahedron_ncc_subrule(rule, suborder_num, ref suborder_xyz, ref suborder_w); Console.WriteLine(""); Console.WriteLine(" The compressed rule:"); Console.WriteLine(""); Console.WriteLine(" Number of suborders = " + suborder_num + ""); Console.WriteLine(""); Console.WriteLine(" S Sub Weight Xsi1 Xsi2 Xsi3 Xsi4"); Console.WriteLine(""); for (s = 0; s < suborder_num; s++) { Console.WriteLine(" " + (s + 1).ToString(CultureInfo.InvariantCulture).PadLeft(4) + " " + suborder[s].ToString(CultureInfo.InvariantCulture).PadLeft(4) + " " + suborder_w[s].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + suborder_xyz[0 + s * 4].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + suborder_xyz[1 + s * 4].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + suborder_xyz[2 + s * 4].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + suborder_xyz[3 + s * 4].ToString("0.####").PadLeft(8) + ""); } int order_num = NewtonCotesClosed.tetrahedron_ncc_order_num(rule); double[] xyz = new double[dim_num * order_num]; double[] w = new double[order_num]; NewtonCotesClosed.tetrahedron_ncc_rule(rule, order_num, ref xyz, ref w); Console.WriteLine(""); Console.WriteLine(" The full rule:"); Console.WriteLine(""); Console.WriteLine(" Order = " + order_num + ""); Console.WriteLine(""); Console.WriteLine(" O Weight X Y Z"); Console.WriteLine(""); for (o = 0; o < order_num; o++) { Console.WriteLine(" " + (o + 1).ToString(CultureInfo.InvariantCulture).PadLeft(4) + " " + w[o].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + xyz[0 + o * 3].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + xyz[1 + o * 3].ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + xyz[2 + o * 3].ToString("0.####").PadLeft(8) + ""); } }
private static void test04() //****************************************************************************80 // // Purpose: // // TEST04 tests TETRAHEDRON_NCC_RULE. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 31 January 2007 // // Author: // // John Burkardt // { int a; const int dim_num = 3; Console.WriteLine(""); Console.WriteLine("TEST04"); Console.WriteLine(" TETRAHEDRON_NCC_RULE returns the points and weights of"); Console.WriteLine(" an NCC rule for the unit tetrahedron."); Console.WriteLine(""); Console.WriteLine(" This routine uses those rules to estimate the"); Console.WriteLine(" integral of monomomials in the unit tetrahedron."); int rule_num = NewtonCotesClosed.tetrahedron_ncc_rule_num(); const double volume = 1.0 / 6.0; for (a = 0; a <= 6; a++) { int b; for (b = 0; b <= 6 - a; b++) { int c; for (c = 0; c <= 6 - a - b; c++) { // // Multiplying X**A * Y**B * Z**C by COEF will give us an integrand // whose integral is exactly 1. This makes the error calculations easy. // double coef = 1.0; // for ( i = 1; i <= a; i++ ) // { // coef = coef * i / i; // } int i; for (i = a + 1; i <= a + b; i++) { coef = coef * i / (i - a); } for (i = a + b + 1; i <= a + b + c; i++) { coef = coef * i / (i - a - b); } for (i = a + b + c + 1; i <= a + b + c + 3; i++) { coef *= i; } Console.WriteLine(""); Console.WriteLine(" Integrate " + coef + " * X^" + a + " * Y^" + b + " * Z^" + c + ""); Console.WriteLine(""); Console.WriteLine(" Rule QUAD ERROR"); Console.WriteLine(""); int rule; for (rule = 1; rule <= rule_num; rule++) { int order_num = NewtonCotesClosed.tetrahedron_ncc_order_num(rule); double[] xyztab = new double[dim_num * order_num]; double[] wtab = new double[order_num]; NewtonCotesClosed.tetrahedron_ncc_rule(rule, order_num, ref xyztab, ref wtab); double quad = 0.0; int order; for (order = 0; order < order_num; order++) { double x = xyztab[0 + order * dim_num]; double y = xyztab[1 + order * dim_num]; double z = xyztab[2 + order * dim_num]; // // Some tedious calculations to avoid 0**0 complaints. // double value = coef; if (a != 0) { value *= Math.Pow(x, a); } if (b != 0) { value *= Math.Pow(y, b); } if (c != 0) { value *= Math.Pow(z, c); } quad += wtab[order] * value; } quad = volume * quad; double exact = 1.0; double err = Math.Abs(exact - quad); Console.WriteLine(" " + rule.ToString(CultureInfo.InvariantCulture).PadLeft(8) + " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + err.ToString(CultureInfo.InvariantCulture).PadLeft(14) + ""); } } } } }